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The square of the length of tangent from (3, –4) on the circle x^{2} + y^{2} – 4x – 6y + 3 = 0
[AIEEE2002]
If the two circles (x – 1)^{2} + (y – 3)^{2} = r^{2} and x^{2} + y^{2} – 8x + 2y + 8 = 0 intersect in two distinct points, then
[AIEEE2003]
The lines 2x – 3y = 5 and 3x – 4y = 7 are diameters of a circle having area as 154 sq. units. Then the equation of the circle is
[AIEEE2003]
If a circle passes through the point (a, b) and cuts the circle x^{2} + y^{2} = 4 orthogonally, then the locus of its centre is 
[AIEEE2004]
A variable circle passes through the fixed point A(p, q) and touches xaxis. The locus of the other end of the diameter through A is 
[AIEEE2004]
If the lines 2x + 3y + 1 = 0 and 3x – y – 4 = 0 lie along diameters of a circle of circumference 10p, then the equation of the circle is 
[AIEEE2004]
If the circles x^{2} + y^{2} + 2ax + cy + a = 0 and x^{2} + y^{2} – 3ax + dy – 1 = 0 intersect in two distinct point P and Q then the lines 5x + by – a = 0 passes through P and Q for 
[AIEEE2005]
A circle touches the xaxis and also touches the circle with centre at (0, 3) and radius 2. The locus of the centre of the circle is 
[AIEEE2005]
If a circle passes through the point (a, b) and cuts the circle x^{2} + y^{2} = p^{2 }orthogonally, then the equation of the locus of its centre is 
[AIEEE2005]
If the pair of line ax^{2} + 2(a + b)xy + by^{2} = 0 lie along diameters of a circle and divide the circle into four sectors such that the area of one of the sectors is thrice the area of another sector then
[AIEEE2005]
If thel ines 3x – 4y – 7 = 0 and 2x – 3y – 5 = 0 are two diameters of a circle of area 49p square units, the equation of the circle is 
[AIEEE2006]
Let C be the circle with centre (0,0) and radius 3 units. The equation of the locus of the mid points of the chords of the circle c that subtend an angle of at its centre is 
[AIEEE2006]
Consider a family of circles which are passing through the point (–1, 1) and are tangent to xaxis. If (h,k) are the coordinates of the centre of the circles, then the set of values of k is given by the interval
[AIEEE2007]
The point diametrically opposite to the point P(1, 0) on the circle x^{2} + y^{2} + 2x + 4y – 3 = 0 is 
The circle x^{2} + y^{2} = 4x + 8y + 5 intersects the line 3x – 4y = m at two distinct points if
[AIEEE2010]
The two circles x^{2} + y^{2} = ax and x^{2} + y^{2} = c^{2} (c > 0) touch each other if :
[AIEEE2011]
The length of the diameter of the circle which touches the xaxis at the pint (1, 0) and passes through the point (2, 3)
[AIEEE2012]
The circle passing through (1, –2) and touching the axis of x at (3, 0) also passes through the point :
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